The maximum or minimum of a quadratic function occurs at . If is negative, the maximum value of the function is . If is positive, the minimum value of the function is .

occurs at

Find the value of equal to .

Substitute in the values of and .

Remove parentheses.

Multiply by .

Dividing two negative values results in a positive value.

Replace the variable with in the expression.

Simplify each term.

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Raise to the power of .

Raise to the power of .

Multiply .

Multiply by .

Combine and .

Multiply by .

Find the common denominator.

Multiply by .

Combine.

Write as a fraction with denominator .

Multiply by .

Multiply and .

Multiply by .

Combine fractions.

Combine fractions with similar denominators.

Multiply.

Multiply by .

Multiply by .

Simplify the numerator.

Add and .

Subtract from .

The final answer is .

Use the and values to find where the maximum occurs.

Find the Maximum/Minimum Value f(x)=-x^2-5x-2